The "generic" trend started a few years before WotC with the release of Champions and then the Hero Game system. For miniatures, I'm not so sure. I any event, the LOS system is not all-encompassingly generic because it really only captures the flavour of the 20th century or later, particularly WWII and thereafter.
The point is, the idea isn't about Legions of Steel itself. The idea is to free other creative types from the burden of coming up with a solid game system so as to let them focus on the figs, the history, the fiction and such. It is whimsy to have Commandos, Daleks, Imperial Stormtroopers and Terminators fighting it out on the same board, but that is what makes it so cool! I want to put in place a legal structure so that bit players are not cowwed into hiding.
It would lay the foundation for "official" conversions of the figures between the systems, which is all good because players could choose the system while buying the figs they like. A miniature game should live or die by its miniatures and not by its rules.
Certain interests will want to keep an unbreakable link between their rules and figures but that is either sheer ego, or - to coin a phrase from The Matrix - another level of control.
It's all very Darwinian in that the "good" game systems will evolve to players' satisfaction.
You have to think of what the motivation of, say, GW would be to veto conversions of their figures into LOS?